If you have a lot of observations, however, using the web search is costly to do. ArcGIS is equipped with Geonames Tools toolbox that automates search. Another way to get around is to download the entire data of GeoNames. This page lists the zip files each of which contains all the locations in a particular country (see here to understand which file is for which country). This file can then be merged with your data by location name, which does geo-reference your data.

The list of variables (called fields) in the data (taken from the bottom of this page):